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Since this thread continues to interest people, a request: Do people know more jokes that are erudite? That is, jokes that are related to interesting mathematics in some way. (Not necessarily very abstract mathematics.) The Banach-Tarski joke below is a good example, in my opinion.
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Greg KuperbergNov 22 '09 at 0:11

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I just voted this -1, and I'd like to see the question closed. People have had over a month to enjoy it, and its continued presence on the front page seems to encourage people to post very soft questions. This takes Math Overflow in what I think is a bad direction.
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Tom LeinsterNov 28 '09 at 12:34

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I disagree with Tom. I think some levity is desirable, and MO shouldn't all be serious business.
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Richard DoreDec 10 '09 at 21:50

I've decided to finally put this one out of its misery. All that's happening now is people add new, mostly lame, jokes at the the end, which no one ever reads, and as a result the question keeps bouncing back to the front page. It's time to die. Closed.
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Scott Morrison♦Dec 24 '09 at 2:23

a pure and applied mathematician were sitting in a bar, when they spotted a hot chick 2 meters away. However, this was a weird place where they could take one 1 meter step and each consecutive would have to be half of the length of the previous one.

The pure mathematician was sad because he knew he could never get to the girl. The applied one was happy because he knew that for all practical purposes he can get close enough.

Consider the following scenario: A room with a sink at the far end with a working cold water faucet plus a table with the following items on top – small bucket, ring stand, Bunsen burner, and a pack of matches. The problem is to boil water.

If the individual picks up the bucket from the table, walks to the sink and fills the bucket from the faucet, brings it back to the table, sets it on the ring stand, puts the Bunsen burner under the stand, and then lights the burner and waits for the water to boil … this establishes the base line but does not separate which it the Physicist and which is the Mathematician.

Test scenario 2: The bucket is now sitting on the floor under the table and the problem is again to boil water.

If the individual picks up the bucket from under the table, walks directly to the sink and fills the bucket from the faucet, brings it back to the table, sets it on the ring stand, puts the Bunsen burner under the stand, and then lights the burner and waits for the water to boil … this proves that this individual is the Physicist.

However, if the individual picks up the bucket from under the table and places it back on top of the table thus reducing the current problem to a form that they have previously solved … this proves that this individual is the Mathematician.

What's purple, commutes, and is worshipped twice a night? A bi-nightly venerated Abelian grape. The other answer to "what's purple and commutes?", for the Chicagoans and ex-Chicagoans out there, is "the Evanston Express".
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Hugh ThomasOct 19 '09 at 17:07

An infinite number of mathematicians walk into a bar. The first one orders a beer, the second one orders half a beer, the third one a quarter of beer and so on. After a while of this happening, the bartender says "Come on guys! So many people and not even a couple of beers??".

For actual humour, rather than simply bad puns, I recommend the books:

A Random Walk in Science

More Random Walks in Science

As well as the odd bad pun, they also contain many anecdotes demonstrating that scientists (and mathematicians) are also human. A few that have stuck in my memory: just about every "mathematics of big game hunting" method, the various "proof by ...", a (genuine!) article co-authored by a cat, and a disturbing article on refereemanship.

Check out the book 777 Mathematical Conversation Starters by John de Pillis. The subject of the book is mathematics topics to talk about, but it is also full of interesting quotes, jokes, and cartoons.

In a math party, all were having a good time. y was the dj, everybody was Riemmanly drunk. Then, when the x saw e^x on a corner crying, he asked:
- Hey e^x, why don't you integrate ?
- Because I keep always the same!!!

If we can formalize the property of "being a good math joke" good enough to construct a Turing Machine that checks it, then I think we can conclude they don't exist.

The reason is that in that case we can construct a Turing Machine (say of length N) that checks each possible string, and stops only if a good math joke was found.
The busy beaver function on N establishes an upper bound for the number of strings the machine needs to check until we can conclude that it wouldn't halt (and therefore no good math jokes exist).

Based on empirical evidence, it may be possible that all those cases have already been checked (with negative answer), which implies my thesis.